Post your answer to the April 18, Let's Experiment here. Best, Chris

-- April 18 Thread

a. [100, 15, 5, 10, 15] b. 100 = 0000001 100100 15 = 0001 111 5 = 001 01 10 = 0001 010 c. M_opt = 26.9 = 27

-- April 18 Thread

	M_opt=26.88 = 27

Consider the posting list [100, 115, 120, 130, 145]. (a)The Δ-list for this list: [100,15,5,10,15] (b) a γ-code, [0000001 100100, 0001 111, 001 01, 0001 010, 0001 111 ] (c) Golumb-code using the formula: M_opt=26.88 = 27

-- April 18 Thread

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-- April 18 Thread

a) [100, 15, 5, 10, 15] b) 0000001 100100 | 0001 111 | 001 01 | 0001 010 | 0001 111 c) M_opt = (log(2 - Nt/N))/(-log(1-Nt/N)) = 0.9818526533/-0.03652587602 = 27 q = [k-1/M] r = (k-1) mod m q(k) = 3 r(k) = 18 for k = 100 similarly calculating for other numbers Golomb code: 0001 10010 | 1 01110 | 1 00100 | 1 01001 | 1 01110

-- April 18 Thread

A) \delta list = [100,15,5,10,15] B) 0000001100100 0001111 00101 0001010 0001111 C) M_opt = 27 D) 00001 10010, 01 01110, 01 00100, 01 01001, 01 01110

-- April 18 Thread

Posting list [100,115,120,130,145] Delta list : [100,15,5,10,15] Encoding using Gamma code, 100 = 0000001 100100 15 = 0001 111 5 = 001 01 10 = 0001 010 15 = 0001 111 Gamma endoging -> [0000001 100100 | 0001 111 | 001 01 | 0001 010 | 0001 111] Golomb/Rice code M = 27 q(k) = [3, 0, 0, 0, 0] r(k) = [18,14,4,9,14] Golomb/Rice encoding -> [0001 10010 | 1 01110 | 1 00100 | 1 01001 | 1 01110]

-- April 18 Thread

	M_opt=log(2 - Nt/N))/(-log(1-Nt/N)) = 0.29003/0.01099 ~ 27

Original posting list [100, 115, 120, 130, 145]. Nt = 5, N = 200 (a)The Δ-list: [100,15,5,10,15] (b) a γ-code, [0000001 100000, 0001 111, 001 01, 0001 010, 0001 111 ] (c) Golumb-code using the formula: M_opt=log(2 - Nt/N))/(-log(1-Nt/N)) = 0.29003/0.01099 ~ 27 => [0001 10010, 1 01110, 1 00100, 1 01001, 1 01110]

-- April 18 Thread

 L = [100, 115, 120, 130, 145]

 /_\(L) = [100, 15, 5, 10, 15]

 γ code = [000001 100100, 0001 111, 001 01, 0001 010] 

 M_opt = 0.981/-0.036 = 27

 Golumb code =  [0001 10010, 1 01110, 1 00100, 1 01001, 1 01110]

L = [100, 115, 120, 130, 145] /_\(L) = [100, 15, 5, 10, 15] γ code = [000001 100100, 0001 111, 001 01, 0001 010] M_opt = 0.981/-0.036 = 27 Golumb code = [0001 10010, 1 01110, 1 00100, 1 01001, 1 01110]

-- April 18 Thread

   
   Mopt = log(2-5/200) / -log (1-5/200)
        = 27
   for k=100, q(k) = 99/27 = 14 ,r(k) = 99 mod 27 =18 => 0000000000000 10010
   for k=15, q(k) = 14/27 = 0 ,r(k) = 14 mod 27 =14 => 0 1110
   for k=5, q(k) = 4/27 = 0 ,r(k) = 4 mod 27 =4 => 0 0100
   for k=10, q(k) = 9/27 = 0 ,r(k) = 9 mod 27 =9 => 0 1001
   for k=15, q(k) = 14/27 = 0 ,r(k) = 14 mod 27 =14 => 0 1110

   Golomb code = [0000000000000 10010 | 0 1110 | 0 0100 | 0 1001 | 0 1110]

a) delta-list = [100, 15, 5, 10, 15] b) Gamma code encode = [00000011100100, 000 1 111, 00101, 0001010,000 1 111 ] c) Nt = 5 Mopt = log(2-5/200) / -log (1-5/200) = 27 for k=100, q(k) = 99/27 = 14 ,r(k) = 99 mod 27 =18 => 0000000000000 10010 for k=15, q(k) = 14/27 = 0 ,r(k) = 14 mod 27 =14 => 0 1110 for k=5, q(k) = 4/27 = 0 ,r(k) = 4 mod 27 =4 => 0 0100 for k=10, q(k) = 9/27 = 0 ,r(k) = 9 mod 27 =9 => 0 1001 for k=15, q(k) = 14/27 = 0 ,r(k) = 14 mod 27 =14 => 0 1110 Golomb code = [0000000000000 10010 | 0 1110 | 0 0100 | 0 1001 | 0 1110]